Unsupervised relation extraction (URE) aims to extract relations between named entities from raw text without requiring manual annotations or pre-existing knowledge bases. In recent studies of URE, researchers put a notable emphasis on contrastive learning strategies for acquiring relation representations. However, these studies often overlook two important aspects: the inclusion of diverse positive pairs for contrastive learning and the exploration of appropriate loss functions. In this paper, we propose AugURE with both within-sentence pairs augmentation and augmentation through cross-sentence pairs extraction to increase the diversity of positive pairs and strengthen the discriminative power of contrastive learning. We also identify the limitation of noise-contrastive estimation (NCE) loss for relation representation learning and propose to apply margin loss for sentence pairs. Experiments on NYT-FB and TACRED datasets demonstrate that the proposed relation representation learning and a simple K-Means clustering achieves state-of-the-art performance.